%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:08:47 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 50 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Set1,Set2,Intersection] :
( intersection(Set1,Set2,Intersection)
| ~ member(h(Set1,Set2,Intersection),Set1)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
intersection(b,c,bIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
intersection(a,bIc,aIbIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ intersection(aIb,c,aIbIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [Set1,Element] :
( member(Element,Set1)
| ! [Intersection] :
( ~ member(Element,Intersection)
| ! [Set2] : ~ intersection(Set1,Set2,Intersection) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [Set2,Element] :
( member(Element,Set2)
| ! [Intersection] :
( ~ member(Element,Intersection)
| ! [Set1] : ~ intersection(Set1,Set2,Intersection) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [Intersection,Element] :
( member(Element,Intersection)
| ! [Set1] :
( ~ member(Element,Set1)
| ! [Set2] :
( ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f31,plain,
! [X0,X1,X2] :
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f32,plain,
! [X0,X1,X2] :
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f34,plain,
intersection(b,c,bIc),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
intersection(a,bIc,aIbIc),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
~ intersection(aIb,c,aIbIc),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
( member(h(aIb,c,aIbIc),aIb)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolution,[status(thm)],[f30,f36]) ).
fof(f42,plain,
( member(h(aIb,c,aIbIc),c)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolution,[status(thm)],[f31,f36]) ).
fof(f45,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X1)
| ~ intersection(X0,X1,aIbIc)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[status(thm)],[f41,f27]) ).
fof(f46,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X0)
| ~ intersection(X0,X1,aIbIc)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[status(thm)],[f41,f25]) ).
fof(f49,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X1)
| ~ intersection(X0,X1,aIbIc)
| member(h(aIb,c,aIbIc),c) ),
inference(resolution,[status(thm)],[f42,f27]) ).
fof(f56,plain,
( member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[status(thm)],[f45,f35]) ).
fof(f63,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X0)
| ~ intersection(X0,X1,bIc)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[status(thm)],[f56,f25]) ).
fof(f66,plain,
( member(h(aIb,c,aIbIc),a)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[status(thm)],[f46,f35]) ).
fof(f75,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X0)
| ~ intersection(X0,X1,aIb)
| member(h(aIb,c,aIbIc),a) ),
inference(resolution,[status(thm)],[f66,f25]) ).
fof(f77,plain,
( member(h(aIb,c,aIbIc),bIc)
| member(h(aIb,c,aIbIc),c) ),
inference(resolution,[status(thm)],[f49,f35]) ).
fof(f83,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X1)
| ~ intersection(X0,X1,bIc)
| member(h(aIb,c,aIbIc),c) ),
inference(resolution,[status(thm)],[f77,f27]) ).
fof(f114,plain,
( member(h(aIb,c,aIbIc),b)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[status(thm)],[f63,f34]) ).
fof(f120,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X1)
| ~ intersection(X0,X1,aIb)
| member(h(aIb,c,aIbIc),b) ),
inference(resolution,[status(thm)],[f114,f27]) ).
fof(f139,plain,
( member(h(aIb,c,aIbIc),a)
| member(h(aIb,c,aIbIc),a) ),
inference(resolution,[status(thm)],[f75,f33]) ).
fof(f142,plain,
member(h(aIb,c,aIbIc),a),
inference(duplicate_literals_removal,[status(thm)],[f139]) ).
fof(f185,plain,
( member(h(aIb,c,aIbIc),c)
| member(h(aIb,c,aIbIc),c) ),
inference(resolution,[status(thm)],[f83,f34]) ).
fof(f188,plain,
member(h(aIb,c,aIbIc),c),
inference(duplicate_literals_removal,[status(thm)],[f185]) ).
fof(f190,plain,
( intersection(aIb,c,aIbIc)
| ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolution,[status(thm)],[f188,f32]) ).
fof(f192,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X1)
| ~ member(h(aIb,c,aIbIc),X0)
| ~ intersection(X0,c,X1) ),
inference(resolution,[status(thm)],[f188,f29]) ).
fof(f195,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),aIbIc) ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f36]) ).
fof(f201,plain,
( member(h(aIb,c,aIbIc),bIc)
| ~ member(h(aIb,c,aIbIc),b) ),
inference(resolution,[status(thm)],[f192,f34]) ).
fof(f225,plain,
( member(h(aIb,c,aIbIc),b)
| member(h(aIb,c,aIbIc),b) ),
inference(resolution,[status(thm)],[f120,f33]) ).
fof(f228,plain,
member(h(aIb,c,aIbIc),b),
inference(duplicate_literals_removal,[status(thm)],[f225]) ).
fof(f229,plain,
member(h(aIb,c,aIbIc),bIc),
inference(backward_subsumption_resolution,[status(thm)],[f201,f228]) ).
fof(f232,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X1)
| ~ member(h(aIb,c,aIbIc),X0)
| ~ intersection(X0,b,X1) ),
inference(resolution,[status(thm)],[f228,f29]) ).
fof(f244,plain,
( member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),a) ),
inference(resolution,[status(thm)],[f232,f33]) ).
fof(f247,plain,
member(h(aIb,c,aIbIc),aIb),
inference(forward_subsumption_resolution,[status(thm)],[f244,f142]) ).
fof(f250,plain,
! [X0,X1] :
( member(h(aIb,c,aIbIc),X1)
| ~ member(h(aIb,c,aIbIc),X0)
| ~ intersection(X0,bIc,X1) ),
inference(resolution,[status(thm)],[f229,f29]) ).
fof(f259,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| ~ member(h(aIb,c,aIbIc),a) ),
inference(resolution,[status(thm)],[f250,f35]) ).
fof(f262,plain,
member(h(aIb,c,aIbIc),aIbIc),
inference(forward_subsumption_resolution,[status(thm)],[f259,f142]) ).
fof(f263,plain,
~ member(h(aIb,c,aIbIc),aIbIc),
inference(backward_subsumption_resolution,[status(thm)],[f195,f247]) ).
fof(f277,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f262,f263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:41:41 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.46 % Refutation found
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.49 % Elapsed time: 0.110856 seconds
% 0.11/0.49 % CPU time: 0.692346 seconds
% 0.11/0.49 % Total memory used: 24.699 MB
% 0.11/0.49 % Net memory used: 23.413 MB
%------------------------------------------------------------------------------